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常见 微积分 问题
limit as x approaches infinity of (ln(x))/(\sqrt[3]{x)}
lim
x
→
∞
(
ln
(
x
)
3
√
x
)
麦克劳林 1/(x-1)
maclaurin
1
x
−
1
(\partial)/(\partial x)(x^4+y^4-4x+1y)
∂
∂
x
(
x
4
+
y
4
−
4
x
+
1
y
)
tangent f(x)=5x^{1/2}+x^{3/2},\at x=4
tangent
f
(
x
)
=
5
x
1
2
+
x
3
2
,
at
x
=
4
implicit (dy)/(dx),y^3+y=x
implicit
dy
dx
,
y
3
+
y
=
x
integral of 1/(x^{13)}
∫
1
x
1
3
dx
integral of sec(x)*tan(x)
∫
sec
(
x
)
·
tan
(
x
)
dx
integral of (3x^2-6x+2)
∫
(
3
x
2
−
6
x
+
2
)
dx
tangent f(x)=2-5x^2,(-2,-18)
tangent
f
(
x
)
=
2
−
5
x
2
,
(
−
2
,
−
1
8
)
derivative (x-2)/((x+2)(x-3))
derivative
x
−
2
(
x
+
2
)
(
x
−
3
)
y^'=(2y)/x ,y(1/(sqrt(2)))=5
y
′
=
2
y
x
,
y
(
1
√
2
)
=
5
limit as x approaches 0 of ((x^3))/x
lim
x
→
0
(
(
x
3
)
x
)
integral from-1 to 3 of x
∫
−
1
3
xdx
integral of (2x^3+5x^2-2x+1)
∫
(
2
x
3
+
5
x
2
−
2
x
+
1
)
dx
derivative x(x+1)^{-1}
derivative
x
(
x
+
1
)
−
1
limit as e^{e^x} approaches 0+of (e^{e^x-2})/2
lim
e
e
x
→
0
+
(
e
e
x
−
2
2
)
derivative of cot(6x-x^2)
d
dx
(
cot
(
6
x
−
x
2
)
)
derivative x*sin(1/x)
derivative
x
·
sin
(
1
x
)
面积 y=x^3-11x^2+30x,y=-x^3+11x^2-30x
area
y
=
x
3
−
1
1
x
2
+
3
0
x
,
y
=
−
x
3
+
1
1
x
2
−
3
0
x
derivative f(x)=3-e^{-x}
derivative
f
(
x
)
=
3
−
e
−
x
derivative of \sqrt[3]{7x}
d
dx
(
3
√
7
x
)
derivative ln(sqrt(x))
derivative
ln
(
√
x
)
integral of e^{-x}sqrt(1+1/(e^{2x))}
∫
e
−
x
√
1
+
1
e
2
x
dx
derivative arccot(8y)
derivative
arccot
(
8
y
)
(\partial)/(\partial x)(x^3+y^3+z^3)
∂
∂
x
(
x
3
+
y
3
+
z
3
)
derivative of 2+|x-3|
d
dx
(
2
+
|
x
−
3
|
)
integral of 7/(x-6)
∫
7
x
−
6
dx
integral of-x+5
∫
−
x
+
5
dx
derivative of ln(2x^3)
d
dx
(
ln
(
2
x
3
)
)
(\partial)/(\partial x)((y^2)/(x+y))
∂
∂
x
(
y
2
x
+
y
)
derivative of (sin(xcos(x))/(2x^2))
d
dx
(
sin
(
x
)
cos
(
x
)
2
x
2
)
limit as x approaches infinity+of 5+6/x
lim
x
→
∞
+
(
5
+
6
x
)
2(d^2y)/(dx^2)-14(dy)/(dx)+24y=3sin(4x)
2
d
2
y
dx
2
−
1
4
dy
dx
+
2
4
y
=
3
sin
(
4
x
)
limit as x approaches 2-of e^{3/((2-x))}
lim
x
→
2
−
(
e
3
(
2
−
x
)
)
(dy)/(dx)=sqrt(6y)e^{x+2}
dy
dx
=
√
6
y
e
x
+
2
面积 x^4-2x^2,2x^2,[-2,0]
area
x
4
−
2
x
2
,
2
x
2
,
[
−
2
,
0
]
integral of 5x-x^2
∫
5
x
−
x
2
dx
integral of ((x+2))/((x^2+2x+10)^{5/2)}
∫
(
x
+
2
)
(
x
2
+
2
x
+
1
0
)
5
2
dx
integral from-2 to 0 of (x^3-4x)
∫
−
2
0
(
x
3
−
4
x
)
dx
inverse拉普拉斯 (e^{-2s})/s
inverselaplace
e
−
2
s
s
y^'=2x(1+x^2-y),y(1)=2
y
′
=
2
x
(
1
+
x
2
−
y
)
,
y
(
1
)
=
2
integral of cos^2(x)ln(x)
∫
cos
2
(
x
)
ln
(
x
)
dx
f(x)=(1+x+x^2)^{99}
f
(
x
)
=
(
1
+
x
+
x
2
)
9
9
integral of 1-cos^2(x)
∫
1
−
cos
2
(
x
)
dx
integral of 1/(x^{1.5)}
∫
1
x
1
.
5
dx
f(x)=2cos(sin(x))
f
(
x
)
=
2
cos
(
sin
(
x
)
)
(dy)/(dt)-7/t y=t^5
dy
dt
−
7
t
y
=
t
5
derivative f(x)=(x^2-5x+8)(3x^2-2)
derivative
f
(
x
)
=
(
x
2
−
5
x
+
8
)
(
3
x
2
−
2
)
derivative of 1/(x+y)
d
dx
(
1
x
+
y
)
integral of 6x+12xln(8x)
∫
6
x
+
1
2
x
ln
(
8
x
)
dx
integral of (x^{-2})
∫
(
x
−
2
)
dx
(10y^2-xy)dx+x^2dy=0
(
1
0
y
2
−
xy
)
dx
+
x
2
dy
=
0
limit as x approaches infinity of 6x^2
lim
x
→
∞
(
6
x
2
)
sum from n=0 to infinity of 1/(1+ln(n))
∑
n
=
0
∞
1
1
+
ln
(
n
)
integral from 2 to 3 of 2/(x^2-1)
∫
2
3
2
x
2
−
1
dx
integral of x^2-2x
∫
x
2
−
2
xdx
integral of cx
∫
cxdx
integral from-1 to 1 of 1/2 (3-3x^2)^2
∫
−
1
1
1
2
(
3
−
3
x
2
)
2
dx
f(x)=x^3cos(x)
f
(
x
)
=
x
3
cos
(
x
)
(\partial)/(\partial x)((4x+3)/(4y+1))
∂
∂
x
(
4
x
+
3
4
y
+
1
)
derivative of (ln(x)/(x^{5/4)})
d
dx
(
ln
(
x
)
x
5
4
)
integral of ycos(y)sin^2(y)
∫
y
cos
(
y
)
sin
2
(
y
)
dy
tangent 1/x ,\at x=2
tangent
1
x
,
at
x
=
2
面积 y=e^x,y=e^{3x},x=ln(2),x=ln(3)
area
y
=
e
x
,
y
=
e
3
x
,
x
=
ln
(
2
)
,
x
=
ln
(
3
)
derivative [x+(x+sin^2(x))^5]^7
derivative
[
x
+
(
x
+
sin
2
(
x
)
)
5
]
7
derivative 6(2x^3+3)6x^2
derivative
6
(
2
x
3
+
3
)
6
x
2
integral of (2-4x^2)/(x-x^3)
∫
2
−
4
x
2
x
−
x
3
dx
tangent y=F-x^2-x,\at x=-2
tangent
y
=
F
−
x
2
−
x
,
at
x
=
−
2
derivative f(x)=10sqrt(t)
derivative
f
(
x
)
=
1
0
√
t
y^'=x+4y
y
′
=
x
+
4
y
sum from n=0 to infinity of 2n
∑
n
=
0
∞
2
n
integral from 0 to 1/7 of sqrt(1-49x^2)
∫
0
1
7
√
1
−
4
9
x
2
dx
面积 x+20,x^2
area
x
+
2
0
,
x
2
derivative of (2x+1^2)
d
dx
(
(
2
x
+
1
)
2
)
integral of 6sin^4(x)cos^2(x)
∫
6
sin
4
(
x
)
cos
2
(
x
)
dx
integral of 5x^4y^2+4x^3y^3
∫
5
x
4
y
2
+
4
x
3
y
3
dx
(\partial)/(\partial x)(5+cos(0.5x-t))
∂
∂
x
(
5
+
cos
(
0
.
5
x
−
t
)
)
derivative '(1/(x^2)-9/(x^4))(x+5x^3)
derivative
′
(
1
x
2
−
9
x
4
)
(
x
+
5
x
3
)
integral of 2x(3-x^2)^3
∫
2
x
(
3
−
x
2
)
3
dx
integral of (x^5)/(x^6+6)
∫
x
5
x
6
+
6
dx
limit as x approaches-1 of (x^2)/(x+1)
lim
x
→
−
1
(
x
2
x
+
1
)
(\partial)/(\partial x)(ln(ln(2x+2y)))
∂
∂
x
(
ln
(
ln
(
2
x
+
2
y
)
)
)
integral of (x^2)/(x^2+5)
∫
x
2
x
2
+
5
dx
integral from 0 to pi of xcos(nx)
∫
0
π
x
cos
(
nx
)
dx
inverse拉普拉斯 (s+1)/(s(s^2+2s+5))
inverselaplace
s
+
1
s
(
s
2
+
2
s
+
5
)
tangent (x-1)/(2-x)
tangent
x
−
1
2
−
x
integral from 25 to x of sqrt(1+9t)
∫
2
5
x
√
1
+
9
t
dt
derivative of 6x^2-6x
d
dx
(
6
x
2
−
6
x
)
integral from 1 to 3 of 15r^3ln(r)
∫
1
3
1
5
r
3
ln
(
r
)
dr
y^{''}+2y^'+y=sin(x)+3cos(2x)
y
′
′
+
2
y
′
+
y
=
sin
(
x
)
+
3
cos
(
2
x
)
integral of (9x)^5sqrt((9x)^3+1)
∫
(
9
x
)
5
√
(
9
x
)
3
+
1
dx
integral of (x^2-3)/((x^2+1)(x-1))
∫
x
2
−
3
(
x
2
+
1
)
(
x
−
1
)
dx
t(dy)/(dt)=t^3+18t^3y
t
dy
dt
=
t
3
+
1
8
t
3
y
integral of cos(x)(1+4sin^2(x))
∫
cos
(
x
)
(
1
+
4
sin
2
(
x
)
)
dx
derivative of \sqrt[3]{1-x^2}
d
dx
(
3
√
1
−
x
2
)
tangent f(x)=sqrt(x),\at x=25
tangent
f
(
x
)
=
√
x
,
at
x
=
2
5
derivative of-4/((x-4^2))
d
dx
(
−
4
(
x
−
4
)
2
)
integral of (2x+4)/(x^2+4x+13)
∫
2
x
+
4
x
2
+
4
x
+
1
3
dx
sum from n=0 to infinity of 1400700
∑
n
=
0
∞
1
4
0
0
7
0
0
sum from n=1 to infinity of (5/n)^4
∑
n
=
1
∞
(
5
n
)
4
1
..
1154
1155
1156
1157
1158
..
2459